Waterways licences: Free flowing natural rivers are different to canalised rivers and canals. Scotland is different altogether.
Canals were dug across private land and so are private. Rivers like the Thames have been modified with weirs and locks, authorised by Act of Parliament. Both of these needs a licence, in England and Wales. The cheapest way to get a licence, and one that covers multiple waterways, is to join British Canoeing if you live in England or Canoe Wales if you live in Wales (both give you a licence for England and Wales).
Natural rivers have had a public right of navigation since the Magna Carta, but there are no recent legal cases confirming that (or disputing it). Most canoeists, kayakers, wild swimmers, etc, now assume it to be the case. Many anglers and landowners disagree. There can be conflict. See riveraccessforall.co.uk Also note that you have no right to cross private land to get to the water.
A few rivers, such as the lower Wye, are clearly defined in recent legislation as public rights of navigation.
Lakes are usually private, but the big ones like Windermere and Coniston are public.
In Scotland, you have freedom of access in most cases provided you respect other users. See Scottish Outdoor Access Code. Unpowered craft are exempt from licences for Scottish canals.
I’ve made some slight simplifications but that’s 99% of it.